Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the equation of the parabola that passes through the points $(-3,-14$ ), $(-5,0$ ), and $(2,0$ ). Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.

View step-by-step help

View step-by-step help

Write a quadratic function from its x-intercepts and another point

Full solution

Q. Write the equation of the parabola that passes through the points

(-3,-14

),

(-5,0

), and

(2,0

). Write your answer in the form

y = a(x - p)(x - q)

, where

a

,

p

, and

q

are integers, decimals, or simplified fractions.

Identify x-intercepts: Identify the x-intercepts from the given points. $\newline$ The x-intercepts are the x-values of the points where the y-values are zero. $\newline$ x-intercepts: $-5$ , $2$
Write equation in form: Use the x-intercepts to write the equation in the form $y = a(x - p)(x - q)$ . $\newline$ $p = -5$ $\newline$ $q = 2$ $\newline$ $y = a(x - (-5))(x - 2)$ $\newline$ $y = a(x + 5)(x - 2)$
Find value of 'a': Use the third point $(-3,-14)$ to find the value of 'a'. $\newline$ Substitute $x = -3$ and $y = -14$ into the equation $y = a(x + 5)(x - 2)$ . $\newline$ $-14 = a(-3 + 5)(-3 - 2)$ $\newline$ $-14 = a(2)(-5)$ $\newline$ $-14 = -10a$
Solve for 'a': Solve for 'a'. $\newline$ $-14 = -10a$ $\newline$ $-14 / -10 = a$ $\newline$ $a = 14/10$ $\newline$ $a = 7/5$
Write final equation: Write the final equation of the parabola using the value of $a$ and the x-intercepts. $a = \frac{7}{5}$ $p = -5$ $q = 2$ $y = a(x - p)(x - q)$ $y = \left(\frac{7}{5}\right)(x + 5)(x - 2)$

More problems from Write a quadratic function from its x-intercepts and another point

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 1 month ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 1 month ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 1 month ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 1 month ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 1 month ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 1 month ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago